Syllogism questions test whether a conclusion must follow from a set of statements. Treat every statement as a relationship between groups, not as information about the real world.

Basic statement forms

• All A are B: every member of A belongs to B.
• No A is B: A and B do not overlap.
• Some A are B: at least one member belongs to both groups.
• Some A are not B: at least one A lies outside B.

How to read the statements

Imagine circles for the groups. “All A are B” places A completely inside B. “No A is B” keeps the circles separate. “Some A are B” creates an overlap, while “some A are not B” leaves part of A outside B.

A conclusion follows only when it is true in every possible diagram allowed by the statements. A conclusion that is merely possible does not follow unless the question specifically asks for possibility.

Valid deductions

• All A are B; all B are C; therefore, all A are C.
• Some A are B; all B are C; therefore, some A are C.
• All A are B; no B is C; therefore, no A is C.
• Some A are B; no B is C; therefore, some A are not C.

Rules to remember

• “All A are B” does not mean all B are A.
• “Some A are B” can be reversed: some B are A.
• “No A is B” can be reversed: no B is A.
• Do not assume that a group exists just because an “all” or “no” statement names it.
• Do not combine two “some” statements unless they share a guaranteed common member.

Possibility conclusions

A possibility conclusion is valid when no statement prevents it. For example, from “All poets are dreamers,” it is possible that some dreamers are poets. It is not possible to conclude “some poets are dreamers” unless the existence of poets is given.

A quick solving method

1. Translate each statement into an inclusion, separation, or overlap.
2. Link groups only through statements that force a connection.
3. Test each conclusion independently.
4. Reject reversed “all” statements and conclusions based on assumed existence.
5. For a possibility question, check only whether a contradiction occurs.

Quick revision summary

• Use diagrams or set relationships rather than everyday knowledge.
• All + all creates a chain; some + all carries the “some” forward.
• A negative statement can block an otherwise tempting conclusion.
• “Some” proves existence; “all” and “no” do not.